The asymptotic behavior of threshold models used to describe the evolution of opinion dynamics and the formation of collective actions in social networks is studied. The proposed model introduces a parameter accounting for the level of self-confidence of the agents, which affects the dynamic evolution of the threshold and in turn the way the agents make their decision. The impact that the network topology has on the asymptotic behavior of the system is studied both analytically and via numerical simulation.
A related research line concerns the performance of consensus protocols in the presence of bounded measurement errors. Both static and dynamic weights are considered. Bounds and the maximum deviation from consensus are derived in terms of the structure of the weight matrix and the maximum magnitude of the measurement errors.
You can find more information in the following publications.
References
Dynamic threshold models
Consensus under uncertainty